A piece of copper wire with thin insulation, 200 m long and 1.00 mm in diameter, is wound onto a plastic tube to form a long solenoid. This coil has a circular cross section and consists of tightly wound turns in one layer. If the current in the solenoid drops linearly from 1.60 A to zero in 0.120 seconds, an emf of 80.0 mV is induced in the coil. What is the length of the solenoid, measured along its axis

 N= 3

Explanation:

For this exercise we must use Faraday's law

          E = - dФ / dt

         Ф = B . A = B Acos θ

tje bold indicate vectors. As it indicates that the variation of the field is linear, we can approximate the derivatives

         E = - A cos θ (B - B₀) / t

The angle enters the magnetic field and the normal to the area is zero

         cos 0 = 1

         A = π r²

In the length of the wire there are N turns each with a length L₀ = 2π r

          L = N (2π r)

          r = L / 2π N

    we substitute

          A = L² / (4π N²)

The magnetic field produced by a solenoid is

           B = μ₀ N/L   I

for which

            B₀ = μ₀  N/L   I

The final field is zero, because the current is zero

            B = 0

We substitute

           E = - (L² / 4π N²)  (0 - μ₀ N/L I) / t

           E = μ₀ L I / (4π N t)

           N = μ₀ L I / (4π t E)

The electromotive force is E = 0.80 mV = 0.8 10⁻³ V

let's calculate

           N = 4π 10⁻⁷ 200 1.60 / (4π 0.120 0.8 10⁻³)]

           N  = 320 10⁻⁷ / 9.6 10⁻⁶

           N = 33.3 10⁻¹

          N= 3

b.

explanation:

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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